Abstract
This paper summarizes the details of recently proposed binary locally repairable codes (BLRCs) and their features. The construction of codes over a small alphabet size of symbols is of particular interest for efficient hardware implementation. Therefore, BLRCs are highly noteworthy because no multiplication is required during the encoding, decoding, and repair processes. We explain the various construction approaches of BLRCs such as cyclic code based, bipartite graph based, anticode based, partial spread based, and generalized Hamming code based techniques. We also describe code generation methods based on modifications for linear codes such as extending, shorting, expurgating, and augmenting. Finally, we summarize and compare the parameters of the discussed constructions.
Highlights
Efficient distributed storage systems (DSSs) are considered to be crucial infrastructure for handling big data
We introduce the construction of binary locally repairable codes (BLRCs) with various parameters and motivations, some of which are optimal or near-optimal with respect to the aforementioned bounds
An (n, k ) BLRC code C from Construction (RV) has an all-symbol locality equal to r = 2 and the all-symbol availability profile is given by t = [k − 1, · · ·, k − 1, 2, · · ·, 2, 1, · · ·, 1], where the numbers of (k − 1)s, 2s, and 1s are k, k(k − 3), and k, respectively, and each value denotes the availability for local repair of the ith symbol of a codeword in C
Summary
Efficient distributed storage systems (DSSs) are considered to be crucial infrastructure for handling big data. These systems must be able to reliably store data over a long duration by introducing redundancy and storing data in a distributed manner across several storage nodes, which may be individually unreliable and could generate failures. For efficient and convenient hardware implementation, the construction of codes over a small alphabet size for the stored symbols is of particular interest. In. Section 3, generation methods of LRCs are summarized with respect to individual types and features, with a focus on BLRC.
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